on a rainy day, a girl broke up with her boy friend after being together for eight long years. they decided to separate at the place where everything about them began, at the same time. the boy is due north crying and running at a rate of 5 ft/sec and the girl is walking due east at rate of 1ft/sec thinking if she made the right decision how fast are they separating from each other 5 seconds after they started moving to a new life without each other?
Answers
Given : on a rainy day, a girl broke up with her boy friend after being together for eight long years. they decided to separate at the place where everything about them began, at the same time. the boy is due north crying and running at a rate of 5 ft/sec and the girl is walking due east at rate of 1ft/sec
To Find : how fast are they separating from each other 5 seconds after they started moving to a new life without each other?
Solution
Boy is running in north at rate of 5 ft/sec
girl is walking due east at rate of 1 ft/sec
Distance be boy in 5 secs = 5 * 5 = 25 ft
Distance by girl in 5 secs = 5 * 1 = 5 ft
North and east are perpendicular to each other
Hence net distance = √(25)² + 5² = 5√26 ft
z = x + iy
z² = x² + y² z = net distance , x = girl distance , y = boy distance
2z dz/dt = 2x.dx/dt + 2y.dy/dt
dx/dt = 1
dy/dt = 5
dz/dt at 5 sec
=> 2 (5√26 ) dz/dt = 2(5) * 1 + 2(25)(5)
=> √26 dz/dt = 1 + 25
=> √26 dz/dt = 26
=> dz/dt = √26
they separating from each other 5 seconds at √26 ft/sec ≈ 5.1 ft sec
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